State Space Domain Research Articles

State Space Model Reference Adaptive Control for a Class of Second-Degree Fractional Order Systems with Different Eigenvalues

This study proposes an adaptive control synthesis for a class of second-degree fractional order systems with different eigenvalues in the state-space domain. The proposed fractional order adaptive controller is a generalization of the MRAC controller for the class of scalar fractional order systems. In order to control the fractional order plant, an adaptive state space feedback controller is applied based on the error between the system output and a chosen reference model using a fractional adaptation law to make the fractional order plant track the fractional order reference model. We show that the resulting adaptive regulator is able to stabilize the fractional order second degree system with a satisfying performance. A simulation example illustrating these performance properties is provided along with a comparison with a fractional order sliding mode control (FOSMC) to demonstrate the superiority of the proposed control scheme.

Virtual measurements for exterior vibro-acoustic problems using experimental modal models

This paper presents a virtual sensor scheme for vibroacoustic radiation applications based on experimental modal state-space models and sparse measurements. A Kalman filter is used for the estimation combining data from the acoustical and the structural domain together with the numerical modal process model. It is proposed to use Gramians, as an energy-related measure of a system’s observability which enables assessing the observability of the coupled vibroacoustic system in the modal state-space domain and the physical state domain counterpart. This Gramian-based observability metric reveals modes or states of high observability, which ensure good estimation results in the subsequent estimation. The proposed method is validated using an industrial test setup for which, due to its high complexity, modelling with first-principle techniques is not feasible. The estimation results demonstrate improved performance compared to a pure forward use of the identified model, indicating the effectiveness of the virtual sensor approach. Additionally, the newly proposed Gramian-based observability criterion outperforms state-of-the-art metrics for sensor placement in terms of estimation accuracy for particular states of interest, as demonstrated in a sensor placement task. Overall, this paper provides a promising approach for virtual sensing for vibroacoustic applications, enabling accurate and efficient system monitoring and control.

A Novel Scheduling Algorithm for Improved Performance of Multi-Objective Safety-Critical WSN Using Spatial Self-Organizing Feature Map

Technological advances in the internet of things (IoT) allowed a low-cost, yet small sensor device to operate with limited power in a dynamic harsh environment where human intervention is impossible. The wireless sensor network (WSN) is an example of the IoT in which physical devices’ software and sensors can interconnect to provide application services. It is important that such applications be dependable to meet the required quality of service (QoS) and function as expected. Consequently, the multi-objective optimization (MOO) problem in WSNs aims to address the trade-off among coverage, connectivity, and network lifetime requirements. Node scheduling is one approach of many used to optimize energy in WSNs. The contribution of this work is the proposal of a self-organizing feature map (SOFM) to enhance the node scheduling in WSNs. The proposed SOFM node-scheduling algorithm aims to spatially explore the state space domain and obtain an optimal solution. In our experiment, the proposed SOFM node-scheduling algorithm is evaluated against a comparable algorithm, namely the BAT node-scheduling algorithm, via MATLAB simulator. The results showed that the SOFM node-scheduling algorithm outperformed the latter by 27% and 28% for the maximum and minimum coverage, respectively, with similar performance of 99% of connectivity and network lifetime.

Verification of the Mode Decomposition Technique for Closely Distributed Modal Systems in the State Space Domain.

This study aims to propose and validate the state space mode decomposition technique for precise mode separation of non-classical damping systems and closely distributed modal systems. To assess the reliability and applicability of this technique, a 40-story building with a tuned mass damper is investigated, and acceleration responses measured by the building's health monitoring system are used for the verification of the technique. The mode separation results reveal that the separated modal power spectrum becomes distorted at neighboring natural frequency ranges when the performance index only considers the concentration of power spectral energy at the target natural frequency. However, by introducing an augmented performance index that includes a constraint condition to account for distortion, more accurate mode decomposition can be achieved.

Perfect control for nonminimum-phase unstable systems defined in the multivariable continuous-time state–space framework — An inverse-based approach

In this paper, a new perfect control law dedicated to nonminimum-phase unstable LTI MIMO systems governed in the continuous-time state–space domain is proposed. Two algorithms are investigated, one of which has turned out to be definitely accurate. Henceforth, the inverse model control-based formula can be applied to any right-invertible plants having more input than output variables. Last, not least, through the application of some generalized inverses, the perfect control procedure guarantees the structural stability behavior even for unstable systems. Thus, the notion of the nonminimum-phase property should be understood in terms of a possible achieveability covering the entire class of LTI MIMO continuous-time plants. Theoretical and practical simulation examples performed in the Matlab/Simulink environment confirm the feasibility of the newly introduced approach.

Virtual sensing-based monitoring and maintenance in elevators

This paper presents a virtual sensing approach for monitoring the elevator installations. The aim of the proposed virtual sensing approach is to monitor the condition of elevators without installing additional sensors. The adopted virtual sensing approach comprises a coupled-electromechanical elevator model presented in state space domain and a generalized output equation which includes not only the available measurements but also a set of virtual sensors. This virtual sensing approach employs an observer, and this observer estimates other physical quantities that cannot be directly measured with the already installed sensors. The estimated physical quantities are then employed for the calculation of four easy-to-interpret Key Performance Indicators (KPIs). These four indicators will enable to report the condition and triggers maintenance actions of elevator installations. Two of the indicators are related to the elevator ride quality and the energy efficiency which are currently employed by elevator manufacturers for evaluating their elevators. The rest two indicators are related to guide system diagnosis and electrical traction machine diagnosis. Finally, the proposed procedure is experimentally evaluated, by comparing the KPIs calculated based on the estimated virtual sensors and actual measurements, with the values obtained from the additional set of sensors installed in an elevator test tower.

Three-Dimensional Effect of Feedback Controlled Winglets in Flutter Suppression of Suspension Bridge

To account for the influence of winglet’s arrangement length and installing position along the longitudinal direction of bridge deck, as well as actuators quantities on flutter control effect, a three-dimensional model of deck-winglet system was been derived in state space domain, and a model reduction method was also discussed to enhance control efficiency. Then, a suspension bridge with a main span of 3[Formula: see text]000[Formula: see text]m was used to investigate the control effect of active winglets, and to explore the influence of winglet length and actuator quantity on flutter control effect. Finally, the flutter and buffeting performance of winglet itself was investigated. The simulation results shows that the modes involved in flutter analysis should be determined according to mode-energy participation ratio. When installing a pair of winglets whose width is 10% of bridge deck, the critical wind speed of bridge deck may be twice of a non-controlled condition. In addition, the critical wind speed increases by increasing the length of winglets and actuator quantity. However, the critical wind speed may remain constant once the winglet length and actuator quantity exceed a critical value. By ensuring the critical wind speed of winglet itself is higher than bridge deck, winglet’s width should be less than 10% of bridge deck’s width, and the independent length winglet is proposed to be shorter than 15% of the length of center span of bridge deck.

Including connecting elements into the Lagrange multiplier state-space substructuring formulation

This paper extends the inverse substructuring (IS) approach into the state-space domain and presents a novel state-space substructuring (SSS) technique that embeds the dynamics of connecting elements (CEs) in the Lagrange Multiplier State-Space Substructuring (LM-SSS) formulation via compatibility relaxation. This coupling approach makes it possible to incorporate into LM-SSS connecting elements that are suitable for being characterized by inverse substructuring (e.g. rubber mounts) by simply using information from one of its off diagonal apparent mass terms. Therefore, the information obtained from an in-situ experimental characterization of the CEs is enough to include them into the coupling formulation. Moreover, LM-SSS with compatibility relaxation makes it possible to couple an unlimited number of components and CEs, requiring only one matrix inversion to compute the coupled state-space model (SSM). Two post-processing procedures to enable the computation of minimal-order coupled models by using this approach are also presented. Numerical and experimental substructuring applications are exploited to prove the validity of the proposed state-space realization of IS and the inclusion of CEs into the LM-SSS formulation via compatibility relaxation. It is found that the IS approach can be accurately applied on state-space models representative of components linked by CEs to identify models representative of the diagonal apparent mass terms of the CEs, provided that the CEs can be accurately characterized by the underlying assumptions of IS. In this way, state-space models representative of experimentally characterized CEs can be found without performing decoupling operations. Hence, these models are not contaminated with spurious states. Furthermore, it was found that the developed coupling approach is reliable, when the dynamics of the CEs can be accurately characterized by IS, thus making it possible to compute reliable coupled models that are not composed by spurious states.

Thermal denitration of sodium nitrate in a fluidized bed reactor: Optimization of process parameters and application of S-statistics for fluidization state monitoring

A voluminous liquid waste stream is generated as sodium nitrate (NaNO3) solution in Spent Nuclear Fuel Reprocessing Plants. Fluidized bed thermal denitration is a strong contender among various disposal options for this stream. In the present work experimental investigations on thermochemical denitration of NaNO3 have been carried out in an 80 NB laboratory scale fluidized bed reactor. Carbon based reductant was utilized to convert NaNO3 to sodium carbonate (Na2CO3) as well as to reduce denitration temperature. The operating parameters were optimized for maximum conversion of NaNO3 and 99.13% denitrification has been achieved. Pressure fluctuation across bed was also recorded and analysed in the state space domain employing attractor comparison technique. This technique computes a statistical metric ‘S’, as a measure of the fluidization state in the fluidized bed reactor and can be used for early detection of agglomeration in the bed. The sensitivity and early agglomeration detection capability of S-statistics are illustrated with experimental results for a liquid-sprayed gas fluidized bed.

Deep Reinforcement Learning for Integrated Non-Linear Control of Autonomous UAVs

In this research, an intelligent control architecture for an experimental Unmanned Aerial Vehicle (UAV) bearing unconventional inverted V-tail design, is presented. To handle UAV’s inherent control complexities, while keeping them computationally acceptable, a variant of distinct Deep Reinforcement Learning (DRL) algorithm, namely Deep Deterministic Policy Gradient (DDPG) is proposed. Conventional DDPG algorithm after being modified in its learning architecture becomes capable of intelligently handling the continuous state and control space domains besides controlling the platform in its entire flight regime. Nonlinear simulations were then performed to analyze UAV performance under different environmental and launch conditions. The effectiveness of the proposed strategy is further demonstrated by comparing the results with the linear controller for the same UAV whose feedback loop gains are optimized by employing technique of optimal control theory. Results indicate the significance of the proposed control architecture and its inherent capability to adapt dynamically to the changing environment, thereby making it of significant utility to airborne UAV applications.

Verifying Provable Stability Domains for Discrete-Time Systems Using Ellipsoidal State Enclosures

Stability contractors, based on interval analysis, were introduced in recent work as a tool to verify stability domains for nonlinear dynamic systems. These contractors rely on the property that - in case of provable asymptotic stability - a certain domain in a multi-dimensional state space is mapped into its interior after a certain integration time for continuous-time processes or after a certain number of discretization steps in a discrete-time setting. However, a disadvantage of the use of axis-aligned interval boxes in such computations is the omnipresent wrapping effect. As shown in this contribution, the replacement of classical interval representations by ellipsoidal domain enclosures reduces this undesirable effect. It also helps to find suitable ratios for the edge lengths if interval-based domain representations are investigated. Moreover, ellipsoidal domains naturally represent the possible regions of attraction of asymptotically stable equilibrium points that can be analyzed with the help of quadratic Lyapunov functions, for which stability criteria can be cast into linear matrix inequality (LMI) constraints. For that reason, this paper further presents possible interfaces of ellipsoidal enclosure techniques with LMI approaches. This combination aims at the maximization of those domains that can be proven to be stable for a discrete-time range-only localization algorithm in robotics. There, an Extended Kalman Filter (EKF) is applied to a system for which the dynamics are characterized by a discrete-time integrator disturbance model with additive Gaussian noise. In this scenario, the measurement equations correspond to the distances between the object to be localized and beacons with known positions.

Bayesian analysis of multiple break-points threshold ARMA model with exogenous inputs

In this paper, we introduce a Bayesian statistical inference approach for multiple break-points threshold autoregressive moving average model with exogenous inputs (MB-TARMAX) which change in state space and time domain. Based on the appropriate prior information of parameters, we give the full conditional posterior distribution of parameters including the thresholds and break-points. In order to obtain the estimates of parameters, we employ the Markov chain Monte Carlo (MCMC) method via Gibbs sampler with Metropolis-Hastings algorithm. Compared with Metropolis-Hastings algorithm, we apply Hamiltonian Monte Carlo algorithm to avoid the slow space exploration from simple random walk and improve the sampling efficiency. As applications, we demonstrate the effectiveness of our method from simulation experiments and a real example.

Kalman filter–random forest‐based method of dynamic load identification for structures with interval uncertainties

It is widely acknowledged that dynamic load identification is a powerful technology for structural health monitoring and reliability analysis. This paper investigates an uncertain dynamic load identification strategy with the combination of the Kalman filter (KF) algorithm and the random forest (RF) model. Enlightened by the concept of the KF, a one-step delayed identification of dynamic loads is completed in the state space domain. The previous loads can be calculated recursively utilizing the previous state estimation and the current displacement observation based on the least square method. In addition, the optimal state estimation will be achieved synchronously with the classical KF algorithm. In terms of inevitable uncertainties, the interval model is introduced to quantify uncertain system parameters and uncertain input loads. To determine the interval load process, the RF surrogate model is constructed to characterize their functional relationship, which is integrated by massive decision trees (DTs). Particularly, Latin hypercube sampling (LHS) and bootstrap sampling (BS) methods are employed to generate training samples for the RF model. The validity and feasibility of the developed methodology are eventually demonstrated by three numerical examples. The results indicate that the proposed approach has an excellent performance in both accuracy and efficiency.

Time Domain State Space Solver for Microwave Systems Based on Laguerre Polynomials

A time-domain state-space solver based on weighted Laguerre polynomials is presented. It is specifically designed for the design optimization of structures excited by predefined pulses. Applications include time-domain reflectometry, radar, and sonar. Such settings have in common that large numbers of systems are to be analyzed for the same excitation. The proposed method features offline-online decomposition, computes the Laguerre expansion of the system response at low cost, and facilitates its transformation to the frequency-domain. The algorithm is validated by a numerical example, involving dispersive material properties. Its performance is compared to that of a Runge-Kutta time-stepping method, with a focus on multi-query settings. A numerical example shows that the computation time of the new method is significantly faster than the Runge-Kutta method.

Comparative analyses of electrical circuits with conventional and revisited definitions of circuit elements: a fractional conformable calculus approach

PurposeThe purpose of this paper is to comparatively analyze the electrical circuits defined with the conventional and revisited time domain circuit element definitions in the context of fractional conformable calculus and to promote the combined usage of conventional definitions, fractional conformable derivative and conformable Laplace transform.Design/methodology/approachThe RL, RC, LC and RLC circuits described by both conventional and revisited time domain circuit element definitions has been analyzed by means of the fractional conformable derivative based differential equations and conformable Laplace transform. The comparison among the obtained results and those based on the methodologies adopted in the previous works has been made.FindingsThe author has found that the conventional definitions-based solution gives a physically reasonable result unlike its revisited definitions-based counterpart and the solutions based on those previous methodologies. A strong agreement to the time domain state space concept-based solution can be observed. The author has also shown that the scalar valued solution can be directly obtained by singularity free conformable Laplace transform-based methodology unlike such state space concept based one.Originality/valueFor the first time, the revisited time domain definitions of resistance and inductance have been proposed and applied together with the revisited definition of capacitance in electrical circuit analyses. The advantage of the combined usage of conventional time definitions, fractional conformable derivative and conformable Laplace transform has been suggested and the impropriety of applying the revisited definitions in circuit analysis has been pointed out.

Design of shifting state-feedback controllers for LPV systems subject to time-varying saturations via parameter-dependent Lyapunov functions

This paper considers the problem of designing a shifting state-feedback controller via quadratic parameter-dependent Lyapunov functions (QPDLFs) for systems subject to symmetric time-varying saturations. By means of the linear parameter varying (LPV) framework and the use of the shifting paradigm and the ellipsoidal invariant theory, it is shown that the solution to this problem can be expressed with linear matrix inequalities (LMIs) which can efficiently be solved via available solvers. Specifically, three hyper-ellipsoidal regions are defined in the state-space domain for ensuring that the control action remains in the linearity region of the actuators where saturation does not occur. Furthermore, the closed-loop convergence speed is regulated online according to the instantaneous saturation limit values through the shifting paradigm concept. The main characteristics of the proposed approach are validated by means of two illustrative examples.

Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition

This paper focuses on the formulation of state–space representations of radiation forces for marine structures using Hankel Singular Value Decomposition (HSVD), a method used to obtain a state–space realization from a Hankel matrix, with the classical definition of the kernel function and its new definition given in this paper. The first part shows the influence of a term commonly neglected and the resulting improvement by taking this term into account. The second part will focus on the feedthrough matrix to understand why some models have none and why some others, such as HSVD, have one. An exact definition of the kernel function will be given underlying its discontinuity and its causality. This study also shows the interest of extrapolating hydrodynamic coefficients before approaching radiation forces by a state–space model.

LQR control on multimode vortex-induced vibration of flexible riser undergoing shear flow

Under the actions of ocean currents and/or waves, deep-sea flexible risers are often subject to vortex-induced vibration (VIV). The VIV can lead to severe fatigue and structural safety issues caused by oscillatory periodic stress and large-amplitude displacement. As flexible risers have natural modes with lower frequency and higher density, a multimode VIV is likely to occur in risers under the action of ocean currents, which is considered as shear flow. To decrease the response level of the VIV of the riser actively, a multimode control approach that uses a bending moment at the top end of the riser via an LQR optimal controller is developed in this study. The dynamic equations of a flexible riser including the control bending moment in shear flow are established both in the time and state-space domains. The LQR controllers are then designed to optimize the objective function, which indicates the minimum cost of the riser's VIV response and control input energy based on the Riccati equation of the closed-loop system under the assumption that the lift coefficient distribution is constant. Finally, the VIV responses of both the original and closed-loop systems under different flow velocities are examined through numerical simulations. The results demonstrate that the designed active control approaches can effectively reduce the riser displacement/angle by approximately 71%–89% compared with that of the original system. Further, for multimode control, the presented mode-weighted control is more effective than the mode-averaged control; the decrease in displacement is approximately 1.13 times than that of the mode-averaged control. Owing to the increase in flow velocity as more and higher-order modes are excited, the VIV response of the original system decreases slightly while the frequency response gradually increases. For the closed-loop system, the response becomes smaller and more complicated, and the efficiency of the controller becomes lower at a certain flow velocity.

A note on the state space representation of aeroelastic systems for time domain analysis

The time domain state space model for describing an aeroelastic system has usually been obtained by using rational function approximations to write unsteady aerodynamics in the time domain. This strategy has been employed by many researchers because the standard form of unsteady aerodynamics is typically computed in the reduced frequency domain with explicit or implied transcendental functions, which do not readily admit to applying frequency to time domain transforms. However, this article demonstrates that the unsteady aerodynamics do not need to be explicitly written in the time domain when the purpose is to obtain a state space model for aeroelastic analysis. A basic and classical result from the linear algebra is employed for constructing a constant dynamic matrix by using the pair of eigenvalues and eigenvectors obtained iteratively from the pk method. The results show that the new approach provides accurate results for linear dynamic aeroelastic models described in either physical or generalized coordinates.

Impedance Parameters Estimation of An RLCM Ladder Network Using Subspace and Similarity Transformation Approach

ABSTRACT Numerous physical systems such as transformers, sensors, and biomaterials are analysed using their equivalent ladder network model. Impedance parameters of a ladder network consist of combinations of resistances, inductances, and capacitances. Accurately determining any device impedance parameters directly from the measured time-domain input-output data is challenging. The use of non-linear optimization algorithms does not always work due to the problem being ill-conditioned. Also, the obtained parameters may not be physically realizable. In this work, the problem is approached from a black-box system identification point of view, followed by a physical parameter extraction step. The necessary current and voltage equations obtained from first principles are utilized to build a physical model in the state-space domain. With the use of a subspace system identification algorithm, the black-box parameter matrices are determined from input-output data, which do not correspond to the physical parameter matrices. However, both sets of parameters can be related through a similarity transformation matrix, leading to the extraction of the physical parameters. The novelty of the approach lies in solving the non-linear parameter estimation problem linearly without initialization. The presence of mutual inductances between various transformer winding sections makes its ladder network the most complex one. Therefore, in this paper, the ladder network model of a transformer winding is considered. As an example of the methodology, a six-section transformer ladder network is simulated and the parameter estimation results are used to validate the proposed algorithm. The same approach can be applied to estimate any other device impedance parameters.